I have configured each department to use the template for that department and each email address is assigned to the correct department.

If an email is sent to [email]hr@domain.com[/email] I would expect osTicket to send an email from the hr template using the [email]hr@domain.com[/email] email address.

What's happening is that any emails sent to [email]hr@domain.com[/email] and [email]billing@domain.com[/email] are assigned to the support department and get the auto-response from the support department... they are not being assigned to the department associated to the incoming email address.

the wiki says the behavior should be as I expect:Routing Incoming Emails

Setting up your system to accept emails varies from system to system and depends on your personal preference. osTicket currently supports piping (aliases) and POP3/IMAP polling methods for routing incoming emails. Tickets are routed to the department and assigned a default priority associated with the email.

Actually what I'm saying is that the wiki documentation should reflect the current version (1.7ST) which you are not using. Since the 1.6ST release (in 2010) I do not recall anyone else reporting the behavior that you are reporting. While its entirely possible that it went completely unnoticed or that I am not remembering someone posting about it... regardless the solution would be to upgrade to 1.7ST.